Inversion of geophysical data is commonly employed in the oil and gas industry as an exploration tool. Decisions regarding whether to drill exploratory wells in specific locations are often made by interpreting maps and images that have been constructed from geophysical data (e.g., seismic reflection, gravity). These data are collected over both land and marine prospects and processed with techniques specific to the type of data being measured and then sometimes inverted to produce models of the subsurface (e.g., reflectivity structure, density structure, etc.). Inversion is the process of inferring a subsurface model from data. Inversion of active seismic, controlled source electromagnetic (CSEM), and gravity data are often used—although typically independently—in the oil and gas industry.
The three components of a typical geophysical data inversion are: (i) data acquired from the field (henceforth called observed data) (ii) a forward simulator to predict data as a function of model parameters and (iii) a numerical mechanism to update model parameters in order to reduce misfit between the observed and predicted data. FIG. 1 shows the steps followed in a typical inversion process. An initial model 11 containing the best guess for the inversion parameters (such as electrical conductivity, seismic velocity, impedance, density, magnetization, etc) is provided to an inversion algorithm 12. Based on the calculated difference between observed data 17 and the data predicted (14) by a forward model 13 as a function of the model parameters, the inversion algorithm suggests an update 15 to the model parameters. This step is typically driven by a mathematical optimizer, which calculates the model update based on the sensitivity of the error function of the predicted and observed data to the model parameters. The model parameters represent a discretized version of the space of interest for inverting for physical properties and may take a variety of forms, including values at the vertices of either regular or irregular grids, values specified or interpolated between surfaces, or values to be interpolated within grids. For example, in the case of 3D CSEM inversion, the model parameters might be a 3D conductivity grid. Various model parameterizations might be used such as finite elements or boundary elements. The inversion process is typically iterative. At the end of each iteration, a termination condition is checked to decide whether to continue the iterations or stop with the then current model becoming a final model 18. This termination condition may be as simple as testing whether the model misfit 16 has dropped below a predefined value, or may involve manual intervention by observing the model updates during the iterative process. The geophysicist might manually intervene, for example, to apply alternate initial models to test hypotheses or to reconcile the inverted model with additional information.
Geophysical data inversion is a challenging process, both in terms of computational expense as well as the ill-posed nature of the problem. Despite these challenges, geophysicists in the oil and gas industry regularly use some form of inversion mechanism for data collected in the field to influence drilling decisions. However, there remains significant uncertainty in predicting the properties of the subsurface (such as structure and fluid type) through inversion of a specific type of data set. Several governing factors go into determining whether an accurate enough inversion can be performed, such as the type and quality of the observed data (measurement noise level) and the physical properties of the subsurface that are to be predicted, to name a few. Each geophysical data type may predict a different physical property, and the resolution attainable for the individual parameters may also be very different. Given these facts, the idea to jointly invert these observed data has emerged. Joint inversion involves using multiple geophysical data sets that constrain different earth properties and combining them in a way that reduces the uncertainty in predicting the earth properties.
FIG. 1 also shows the process of joint inversion, which is conceptually similar to geophysical inversion of individual data types. The difference between the two is that the numerical machinery or algorithm for joint inversion deals with multiple geophysical data simultaneously (indicated by the layering of box 17). Consequently, the geoscientist needs to use multiple forward simulators (indicated by the layering of box 13), one for each data type, possibly involving different physics and even different model representations for each data type. At each iteration of the inversion, a call to every forward simulator is made to predict each type of observed geophysical data, and a combined misfit is calculated. The inversion algorithm then suggests a model update based on this combined misfit. The update mechanism may take into account a priori information such as data uncertainty or model smoothness. How the data are combined, and over what space the inversion parameters are defined depends on the particular choice of the joint inversion implementation, but the main concept encapsulated by FIG. 1 does not change significantly. Joint inversion of several geophysical data types results in a consistent earth model that explains all the geophysical data simultaneously. Next are described briefly some of the methods of joint inversion of geophysical data that have appeared in publications. The model in FIG. 1 may be equivalently thought of as comprising all of the geophysical parameters of interest, such as conductivity, density, shear modulus, bulk modulus, or other parameters or as comprising a set of parameter models, one model for each parameter type of interest. In general, geophysical parameters may be anisotropic.
Hoversten et al., (2006) investigate an algorithm for one-dimensional joint inversion of CSEM and seismic reflection data using synthetic data instead of observed data. They implement a local optimization algorithm, which uses local sensitivity information of the data misfit to the model parameters to suggest updates to the model parameters. They state that global (derivative-free) methods are too computationally expensive for 3D problems. The distinction between local and global methods, along with their relative advantages and disadvantages is described below in this document.
Hu et al. (2009) employ what they term a cross-gradient approach to perform joint inversion of 2D synthetic electromagnetic and seismic data. Their approach exploits the structural similarity that is occasionally seen between the conductivity image and the P-wave velocity image, and enforces this similarity in the form of a constraint on the joint inversion solution. The inversion algorithm updates conductivity and velocity in an alternating fashion while maintaining the structural similarity until the combined CSEM and seismic misfit drops below a predetermined limit.
Chen and Dickens (2007) use a global optimization method (Markov Chain Monte Carlo) to analyze the uncertainties in joint seismic-CSEM inversions, but restrict themselves to 1D synthetic data.
Thus although joint inversion is being investigated as a potential approach for reducing the uncertainty or ambiguity associated with geophysical inversion, there is a need for a more computationally efficient way to perform it. The present invention satisfies this need.